1. Technical Field
The present invention generally relates to wireless communication systems, and particularly relates to controlling multiple-antenna transmission in a wireless communication network, e.g., controlling the precoding operation and selecting the modulation and channel coding rates for Multiple-Input-Multiple-Output (MIMO) transmission.
2. Background
The availability of certain information about (propagation) channel state at the transmitter plays a crucial role in attaining the highest possible spectral efficiency for a wireless communication system with multiple transmit antennas. For example, E. Telatar, “Capacity of multi-antenna Gaussian channels,” Euro. Trans. Telecomm. ETT, vol. 10, no. 6, pp. 585-596, November 1999, demonstrates that substantial gains in capacity can be achieved with multiple antennas when accurate information about the instantaneous channel state is available at the transmitter.
Feedback of instantaneous channel states from targeted receivers to the transmitter represents a known mechanism for providing accurate channel state information, and such feedback may be necessary, such as in Frequency-Division Duplex (FDD) systems where the instantaneous channel states in uplink and downlink are not directly related. Problematically, however, the potential number and complexity of the propagation channels existent in multi-antenna (e.g., MIMO) systems can require significant amounts of channel feedback, which may not be practicable and undesirable in any case. Moreover, even beginning with the questionable assumption that receivers can estimate instantaneous channel states with the requisite accuracy, feedback delays, including computational and signal transmit delays, guarantee that channel feedback obtained at the transmitter lags the actual states observed at the receiver. As such, transmit adjustments do not match the actual instantaneous channel states at the targeted receivers.
As a departure from using instantaneous channel states as a basis for multi-antenna transmission control, some research has instead considered optimal transmission schemes that use long-term statistical information of the propagation channel(s). Unlike instantaneous channel state information which varies at the rate of fast fading, statistical information about the channel varies at a much slower rate (e.g. at the rate of slow fading (shadowing) or at the rate of change in angles of departure/arrival). Consequently, it is much more affordable—in terms of computational and signaling overhead—to accurately feed back statistical channel information from the targeted receivers for corresponding multi-antenna transmission control.
Although basing transmission control on channel statistics feedback significantly reduces the amount and complexity of channel feedback signaling from the targeted receivers, implementing such control is not without its challenges. In practice, the computation of various parameters required for optimal multi-antenna transmission based on channel statistics is often much more difficult than computing them based on instantaneous channel knowledge.
For example, a number of papers present information related to determining the optimal linear precoding matrix Fopt that maximizes the ergodic capacity of a flat MIMO channel with nT transmit antennas and nR receive antennas. Such papers include, E. Visotsky and U. Madhow, “Space-Time Transmit Precoding with Imperfect Feedback,” IEEE Trans. on Info. Thy., vol. 47, pp. 2632-2639, September 2001; S. H. Simon and A. L. Moustakas, “Optimizing MIMO Antenna Systems with Channel Covariance Feedback,” IEEE JSAC, vol. 21, pp. 406-417, April 2003; and A. M. Tulino, A. Lozano, S. Verdu, “Capacity-Achieving Input Covariance for Single-User Multi-Antenna Channels,” IEEE Trans. on Wireless Comm., vol. 5, pp. 662-671, March 2006.
According to various ones of these teachings, Fopt may be calculated as,
                              F          opt                =                                                            arg                            ⁢              max                                                      tr                ⁢                                  {                                                            ∑                      f                                        ⁢                                          FF                      H                                                        }                                            ≤              1                                ⁢                                    E              ⁡                              [                                  log                  ⁢                                                                          ⁢                                      det                                    ⁢                                      (                                          I                      +                                                                        HFF                          H                                                ⁢                                                  H                          H                                                                                      )                                                  ]                                      .                                              Eq        .                                  ⁢                  (          1          )                    More particularly, it has been shown that the optimal precoding matrix can be written asFopt=UD(√{square root over (p1)}, √{square root over (p2)}, . . . , √{square root over (pnT)}),  Eq. (2)where U denotes a matrix whose columns are the eigenvectors of EHHH, D(√{square root over (p1)}, √{square root over (p2)}, . . . , √{square root over (pnt)}) denotes a diagonal matrix with {√{square root over (pj)}}j=1nT as the diagonal elements, and where pj denotes the portion of power assigned to the jth eigen-transmission-mode that corresponds to the jth column of U.
Within the context of the above framework, it has been further shown that the relative power levels {pj}j=1nT must satisfy the following conditions:
                              p          j                =                  {                                                                                                                1                      -                                              E                        ⁡                                                  [                                                      MMSE                            j                                                    ]                                                                                                                                    ∑                                                  i                          =                          1                                                                          n                          T                                                                    ⁢                                              (                                                  1                          -                                                      E                            ⁡                                                          [                                                              MMSE                                i                                                            ]                                                                                                      )                                                                                                                                                        if                      ⁢                                                                                          ⁢                                              E                        ⁡                                                  [                                                      SINR                            j                                                    ]                                                                                      >                                                                  ∑                                                  i                          =                          1                                                                          n                          T                                                                    ⁢                                              (                                                  1                          -                                                      E                            ⁡                                                          [                                                              MMSE                                i                                                            ]                                                                                                      )                                                                                                                                          0                                                  otherwise                                                      ,                                                  ⁢            where                                              Eq        .                                  ⁢                  (          3          )                                                                                            MMSE                j                            =                              1                -                                                      p                    j                                    ⁢                                                                                                              h                          ~                                                j                        H                                            ⁡                                              (                                                                              Q                            j                                                    +                                                                                    p                              j                                                        ⁢                                                                                          h                                ~                                                            j                                                        ⁢                                                                                          h                                ~                                                            j                              H                                                                                                      )                                                                                    -                      1                                                        ⁢                                                            h                      ~                                        j                                                                                                                                          =                                  1                                      1                    +                                                                  p                        j                                            ⁢                                                                        h                          ~                                                j                        H                                            ⁢                                              Q                        j                                                  -                          1                                                                    ⁢                                                                        h                          ~                                                j                                                                                                        ,                                                          Eq        .                                  ⁢                  (          4          )                                                              SINR            j                    =                                                    h                ~                            j              H                        ⁢                          Q              j                              -                1                                      ⁢                                          h                ~                            j                                      ,                            Eq        .                                  ⁢                  (          5          )                                                              Q            j                    =                      I            +                                          ∑                                  i                  ≠                  j                                            ⁢                                                                    h                    ~                                    j                                ⁢                                                      h                    ~                                    j                  H                                                                    ,                            Eq        .                                  ⁢                  (          6          )                    and {{tilde over (h)}j}j=1nT are the column vectors of the transformed channel {tilde over (H)}≡HU=[{tilde over (h)}1,{tilde over (h)}2, . . . ,{tilde over (h)}nT]. Note that since the term MMSEj depends on {pj}j=1nT, the relative power levels {pj}j=1nT are only implicitly defined.
An iterative algorithm has been proposed for computing {pj}j=1nT based on the joint probability distribution, denoted by p({tilde over (H)}), of {tilde over (H)} (or, alternatively, a joint probability distribution of H). As a first step, the algorithm initializes {pj(0)}j=nT such that Σj=1nTpj(0)=1 (e.g. by setting pj(0)=1/nT for all j). Next, the algorithm iterates the fixed point equation until the solution converges:
                                          p            j                          (                              k                +                1                            )                                =                                                                      1                  -                                      E                    ⁡                                          [                                              MMSE                        j                                                  (                          k                          )                                                                    ]                                                                                                            ∑                                          i                      =                      1                                                              n                      T                                                        ⁢                                      (                                          1                      -                                              E                        ⁡                                                  [                                                      MMSE                            j                                                          (                              k                              )                                                                                ]                                                                                      )                                                              ⁢                                                          ⁢              for              ⁢                                                          ⁢              j                        =            1                          ,        2        ,        …        ⁢                                  ,                  n          T                                    Eq        .                                  ⁢                  (          7          )                    where MMSEj(k) are computed based on Eq. (4) with pj set to equal pj(k).
At this point, the algorithm stops if, for every j such that pj has converged to zero in the above step,
                              E          ⁡                      [                          SINR              j                        ]                          ≤                              ∑                          i              =              1                                      n              T                                ⁢                                    (                              1                -                                  E                  ⁡                                      [                                          MMSE                      i                                        ]                                                              )                        .                                              Eq        .                                  ⁢                  (          8          )                    Otherwise, set pj=0 for j that corresponds to the lowest value of E[SINRj].
Execution of the steps involving Eq. (7) and Eq. (8) requires computation of several essential quantities, including:
                                          E            ⁡                          [                              MMSE                j                            ]                                =                      ∫                                          1                                  1                  +                                                            p                      j                                        ⁢                                                                                                                        h                            ~                                                    j                          H                                                (                                                  I                          +                                                                                    ∑                                                              i                                ≠                                j                                                                                      ⁢                                                                                          p                                i                                                            ⁢                                                                                                h                                  ~                                                                i                                                            ⁢                                                                                                h                                  ~                                                                i                                H                                                                                                                                    )                                                                    -                        1                                                              ⁢                                                                  h                        ~                                            j                                                                                  ⁢                              p                ⁡                                  (                                      H                    ~                                    )                                            ⁢                              ⅆ                                  H                  ~                                                                    ,                                  ⁢        and                            Eq        .                                  ⁢                  (          9          )                                                  E          ⁡                      [                          SINR              j                        ]                          =                  ∫                                                                                          h                    ~                                    j                  H                                (                                  I                  +                                                            ∑                                              i                        ≠                        j                                                              ⁢                                                                  p                        i                                            ⁢                                                                        h                          ~                                                i                                            ⁢                                                                        h                          ~                                                i                        H                                                                                            )                                            -                1                                      ⁢                                          h                ~                            j                        ⁢                          p              ⁡                              (                                  H                  ~                                )                                      ⁢                          ⅆ                              H                ~                                                                        Eq        .                                  ⁢                  (          10          )                    
The computation of Eq. (9) and Eq. (10) requires the joint probability distribution p({tilde over (H)}) of the instantaneous channel state {tilde over (H)}, which is difficult, if not impossible, to determine even at the receiver, not to mention the transmitter. While the integrals included in these equations of interest can be approximated by averaging over many realizations of {tilde over (H)} observed at the receiver, that approach includes further complications. Because the quantities of interest depend not only on {tilde over (H)}, but also on the allocated power levels {pj}j=1nT, these quantities need to be evaluated for different values of {pj}j=1nT in order to compute the optimal power levels. As a result, multiple and/or large sets of realizations of {tilde over (H)} would need to be stored in the working memory (e.g., RAM) of a targeted receiver. In practice, however, it is undesirable to require sufficient memory and computational power in the targeted receivers to carry out the above algorithm for computation of optimal transmit preceding values.
Besides the computation of preceding weights for multi-antenna transmission, the selection of proper modulation and channel coding rates for each transmission stream based on channel statistics to date has not been adequately addressed. Such considerations depend on the kind of detection algorithm, e.g., successive-interference-cancellation (SIC), being employed at the targeted receiver(s).